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  2. Limit (category theory) - Wikipedia

    en.wikipedia.org/wiki/Limit_(category_theory)

    If J = 1, the category with a single object and morphism, then a diagram of shape J is essentially just an object X of C. A cone to an object X is just a morphism with codomain X . A morphism f : Y → X is a limit of the diagram X if and only if f is an isomorphism .

  3. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

  4. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...

  5. Cauchy–Hadamard theorem - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Hadamard_theorem

    In mathematics, the Cauchy–Hadamard theorem is a result in complex analysis named after the French mathematicians Augustin Louis Cauchy and Jacques Hadamard, describing the radius of convergence of a power series.

  6. Nested intervals - Wikipedia

    en.wikipedia.org/wiki/Nested_intervals

    Put into words, property 1 means, that the intervals are nested according to their index. The second property formalizes the notion, that interval sizes get arbitrarily small; meaning, that for an arbitrary constant ε > 0 {\displaystyle \varepsilon >0} one can always find an interval (with index N {\displaystyle N} ) with a length strictly ...

  7. Content (measure theory) - Wikipedia

    en.wikipedia.org/wiki/Content_(measure_theory)

    Then the content of a set of positive integers is the average value of the sequence that is 1 on this set and 0 elsewhere. Informally, one can think of the content of a subset of integers as the "chance" that a randomly chosen integer lies in this subset (though this is not compatible with the usual definitions of chance in probability theory ...

  8. Đỗ Cao Trí - Wikipedia

    en.wikipedia.org/wiki/Đỗ_Cao_Trí

    Lieutenant General Đỗ Cao Trí (20 November 1929 – 23 February 1971) was a general in the Army of the Republic of Vietnam (ARVN) known for his fighting prowess and flamboyant style. Trí started out in the French Army before transferring to the Vietnamese National Army and the ARVN.

  9. Central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Central_limit_theorem

    The distribution of ⁠ X 1 + ⋯ + X n / √ n ⁠ need not be approximately normal (in fact, it can be uniform). [38] However, the distribution of c 1 X 1 + ⋯ + c n X n is close to (,) (in the total variation distance) for most vectors (c 1, ..., c n) according to the uniform distribution on the sphere c 2 1 + ⋯ + c 2 n = 1.